Econometrics Homework 4 Solutions

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1 Econometrics Homework 4 Solutions Computer Question (Optional, no need to hand in) (a) c i may capture some state-specific factor that contributes to higher or low rate of accident or fatality. For example, geographical feature, culture in driving, etc. (b) Pooled OLS with clustered standard errors.. reg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, vce(robust) Linear regression Number of obs = 556 F( 21, 534) = R squared = Root MSE = sb_useage speed speed ba drinkage lnincome age yr yr yr yr yr yr yr yr yr yr yr yr yr yr _cons The seat belt usage here has a positive effect on fatality, which is not as expected. We expect seat belt can save the driver and passengers even when there are accidents. Higher speed limit (the base group has a 55mph limit.) leads to a higher fatality, which make sense, as lower speed can reduce the impact of accidents. A lower blood alchohol limit (missing group is a higher blood alcohol level is 0.1.) is related to a lower fatality, which also makes sense because alcohol reduces the ability of judgement for drivers, which increases number of accidents. A higher legal drinking age is associated to a lower fatality rate, which also makes sense, though the coeffi cient is not significantly different from zero. States with higher income is associated with a lower fatality rate, which makes sense, as richer states may have better roads, or cars better maintained or with better safety measures, or with people driving more carefully. The age effect is not significant and close to zero (it the average age of a state, which has little variation across states). The year dummies 1

2 generally involves small coeffi cients, and there is no clear trend over the decade. (c) Random Effect Estimator:. *Random effect model. xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, re vce(robust) Random effects GLS regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = Obs per group: min = 8 between = avg = 10.9 overall = max = 15 Wald chi2(21) = corr(u_i, X) = 0 (assumed) Prob > chi2 = (Std. Err. adjusted for 51 clusters in fips) fatalityrate Coef. Std. Err. z P> z [95% Conf. Interval] sb_useage speed speed ba drinkage lnincome age yr yr yr yr yr yr yr yr yr yr yr yr yr yr _cons sigma_u sigma_e rho (fraction of variance due to u_i) The most notable change is the coeffi cient on seat belt usage, from positive to negative, and marginally significant. Coeffi cient on speed65 has also become negative, but still insignificant. The effect of age has changed sign, but it is still very small. (d) Fixed Effect Estimator: 2

3 . xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997, fe vce(robust) Fixed effects (within) regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = Obs per group: min = 8 between = avg = 10.9 overall = max = 15 F(21,50) = corr(u_i, Xb) = (Std. Err. adjusted for 51 clusters in fips) sb_useage speed speed ba drinkage lnincome age yr yr yr yr yr yr yr yr yr yr yr yr yr yr _cons sigma_u sigma_e rho (fraction of variance due to u_i) In terms of order of magnitudes, the random effect and fixed effect models are similar and again seatbelt usage has a negative effect on fatality. However, the effect of income now becomes positive and insignificant, while age is positive and significant. (e) Here we test all the time varying variables:. *first generate the means. egen sb_usem=mean(sb_useage), by(fips). egen speed65m=mean(speed65), by(fips). egen speed70m=mean(speed70), by(fips). egen ba08m=mean(ba08), by(fips). egen drinkm=mean(drinkage21), by(fips). egen lnincm=mean(lnincome), by(fips). egen agem=mean(age), by(fips) 3

4 . xtreg fatalityrate sb_useage speed65 speed70 ba08 drinkage21 lnincome age yr1984 yr1997 sb_usem agem, re vce(robust) Random effects GLS regression Number of obs = 556 Group variable: fips Number of groups = 51 R sq: within = Obs per group: min = 8 between = avg = 10.9 overall = max = 15 Wald chi2(28) = corr(u_i, X) = 0 (assumed) Prob > chi2 = (Std. Err. adjusted for 51 clusters in fips) fatalityrate Coef. Std. Err. z P> z [95% Conf. Interval] sb_useage speed speed ba drinkage lnincome age yr yr yr yr yr yr yr yr yr yr yr yr yr yr sb_usem speed65m speed70m ba08m drinkm lnincm agem _cons sigma_u sigma_e rho (fraction of variance due to u_i). test sb_usem speed65m speed70m ba08m drinkm lnincm agem ( 1) sb_usem = 0 ( 2) speed65m = 0 ( 3) speed70m = 0 ( 4) ba08m = 0 ( 5) drinkm = 0 ( 6) lnincm = 0 ( 7) agem = 0 chi2( 7) = Prob > chi2 = So, we reject the null that c i and regressors are uncorrelated, and we should use fixed effect. (f) Here I use the fixed effect specification. 4

5 ( 1) yr1984 = 0 ( 2) yr1985 = 0 ( 3) yr1986 = 0 ( 4) yr1987 = 0 ( 5) yr1988 = 0 ( 6) yr1989 = 0 ( 7) yr1990 = 0 ( 8) yr1991 = 0 ( 9) yr1992 = 0 (10) yr1993 = 0 (11) yr1994 = 0 (12) yr1995 = 0 (13) yr1996 = 0 (14) yr1997 = 0 F( 14, 50) = 9.82 So we reject the null that there is no time effect. (g). reg d.fatalityrate d.sb_useage d.speed65 d.speed70 d.ba08 d.drinkage21 d.lnincome d.age yr1984 yr1997, vce(robust) noc Linear regression Number of obs = 497 F( 21, 476) = 6.30 R squared = Root MSE = D. sb_useage D speed65 D speed70 D ba08 D drinkage21 D lnincome D age D yr yr yr yr yr yr yr yr yr yr yr yr yr yr

6 . *use difference in year dummies too. reg d.fatalityrate d.sb_useage d.speed65 d.speed70 d.ba08 d.drinkage21 d.lnincome d.age d.yr1984 d.yr1985 d.yr1986 d.y > r1987 d.yr1988 d.yr1989 d.yr1990 d.yr1991 d.yr1992 d.yr1993 d.yr1994 d.yr1995 d.yr1996 d.yr1997, vce(robust) noc Linear regression Number of obs = 497 F( 21, 476) = 6.30 R squared = Root MSE = D. sb_useage D speed65 D speed70 D ba08 D drinkage21 D lnincome D age D yr1984 D yr1985 D yr1986 D yr1987 D yr1988 D yr1989 D yr1990 D yr1991 D yr1992 D yr1993 D yr1994 D yr1995 D yr1996 D yr1997 D The result is similar to Fixed effect estimator. (h) Using FE or FD estimator, it is found that seat belt, lower speed limit, lower alcohol allowance, higher minimum drinking age can reduce fatality rate. (i) Using fixed effect estimates, this means we increase sb_usage from 0.52 to 0.90, the fatality rate then decreases by ( )( ) = If there are million miles travelled per year, then the number of death reduced is This question is taken from Stock and Watson textbook. It comes from the paper Cohen and Einav (2003) "The Effect of Mandatory Seat Belt Laws on Driving Behavior and Traffi c Fatality" The Review of Economics and Statistics, 85(4):